Wide Area Based Precise Point Positioning

Size: px

Start display at page:

Download "Wide Area Based Precise Point Positioning"

Stuart Daniel
6 years ago
Views:

1 Wide Aea Baed Pecie Poin Poiioning Rodigo F. Leando and Macelo C. Sano Geodeic Reeach Laboaoy, Depamen of Geodey and Geomaic Engineeing Univeiy of ew Bunwick, Fedeicon, Canada BIOGRAPHIES Rodigo Leando i a Ph.D. candidae in he Depamen of Geodey and Geomaic Engineeing, Univeiy of ew Bunwick (UB), Canada, whee he ha been a uden ince 24. He hold an M.Sc.Eng. in civil engineeing fom he Univeiy of São Paulo, in São Paulo, Bazil. He ha been involved in eeach in he field of geodey and aellie poiioning. M. Leando ha eceived a be uden pape awad fom he Canadian Geophyical Union and a uden pape awad fom The Iniue of avigaion, boh in 24. In 26 M. Leando ha alo eceived a be peenaion awad fom The Iniue of avigaion. Macelo Sano i an aociae pofeo in he Depamen of Geodey and Geomaic Engineeing a UB. He hold an M.Sc. in geophyic fom he aional Obevaoy in Rio de Janeio, and a Ph.D. in geodey fom UB. He ha been involved in eeach in he field of pace and phyical geodey, GSS, and navigaion ABSTRACT Pecie poin poiioning (PPP) i a poiioning echnique in which a ingle eceive i ued o deemine i coodinae,uing pecie poduc uch a obi and clock. In hi wok we ae dicuing he ambiguiy paamee in PPP, which, fo eveal eaon, i no an inege value, a i happen in cae of double dfeenced obevaion The ambiguiy paamee in PPP include aellie and eceive biae, which have o be adequaely epaaed in ode o obain inege ambiguiie, wha would allow ambiguiie fiing poce. In ode o do o, a new appoach wa inoduced, called hee wide aea pecie poin poiioning. The main idea of hi new appoach he deeminaion of aellie facional biae uing a newok of eceive. In ode o epaae facional biae fom ohe paamee uch a ionopheic delay and ambiguiie, a de-coelaion file wa ceaed, and in epeimen caied ou involving neaby aion, he ionopheic delay deemined wih he de-coelaion file agee vey well wih each ohe Dfeenial eceive-aellie facional biae wee deemined fo fome IGS aion and PR 2 a L1 fequency and howed o be able wih a mean value of -.6 cycle, and andad deviaion of aound.2 cycle. Thi unceainy in meic uni fo L1 fequency i 3.9 cm. ITRODUCTIO Pecie poin poiioning i a poiioning echnique in which a ingle eceive i ued o deemine i coodinae. I i aid o be pecie becaue pecie poduc uch a obi and clock ae ued in he daa poceing. Moe han ha, all neceay coecion hould be aken ino accoun o achieve he be poible accuacy. Such coecion include ide, elaiviic effec, anenna phae cene vaiaion among ohe. Depending on he ype of eceive being ued (e.g. code only o code and phae; ingle o dual fequency), ome of hoe coecion can be diegaded, and alo fuhe pecie poduc migh be needed, uch a ionopheic gid in cae of ingle fequency eceive. If he highe poible accuacy i ageed, a geodeic eceive i ued, wih dual fequency meauemen of peudoange and caie-phae. In hi cae, ohe apec ae alo impoan, uch a eaing he caie-phae a an independen meauemen (ahe han uing hem o imply file he peudoange), wha implicae in ambiguiy paamee eimaion, and alo he eimaion of eidual neual amophee delay (AD), ince AD pedicion model ae no accuae enough fo hi ype of poiioning. The pecie poin poiioning (PPP) obevaion model i pey much a andad model nowaday (hee we ae uing he wod andad becaue mo of PPP package, uch a CSRS-PPP [Téeaul e al. 25], GAPS, P3 [Gao and Chen, 24] and Gipy [Zumbege e al. 1997], ue hi model, wih ionopheic fee combinaion of peudoange and caie-phae. A few dfeence can be found beween hem, uch a he eimaion poce of AD (e.g. a andom walk, o fied value fo given ime ineval). The baic PPP obevaional model i given by: ( dt d) T P = ρ + c +, (1)

2 and ( dt d) + T + λ φ = ρ + c, (2) whee P i he ionopheic fee combinaion of peudoange meauemen, φ i he ionopheic fee combinaion of caie-phae meauemen in meic uni, ρ i he geomeic diance beween aellie and eceive anenna phae cene, c i he peed of ligh, T i he neual amophee delay (whee T and fo opophee), dt and d ae he ionopheic fee eceive and aellie clock eo, epecivelly, λ i he ionopheic fee caie-phae wavelengh and i he ionopheic fee caie-phae ambiguiy paamee. Thi la em i no imply he combinaion of ambiguiie, bu he combinaion of a few em, including ambiguiie, eaon why i i being called hee a ambiguiy paamee. In hi wok we ae dicuing he ambiguiy em in (2). Fo eveal eaon, hi em i no an inege value, a i happen in cae of double dfeenced obevaion, wha make impoible he appoach of fiing ambiguiie in cae of PPP. The moivaion of a wide aea baed PPP (which will be eplained lae in hi pape) i o allow he ecoveing of inege value fo ambiguiy paamee. GAPS GPS daa Analyi and Poiioning Sofwae GAPS (GPS daa Analyi and Poiioning Sofwae) i a ofwae package fo poiioning (by mean of PPP) and daa analyi, which wa developed a UB. One of he main goal of hi developmen ha been o allow he inveigaion of he wide aea PPP appoach; howeve GAPS howed o be much moe veaile han ha, allowing innovaing daa analyi and qualiy conol pocedue. GAPS PPP ue he funcional model given by (1) and (2). The daa poceing i done in an epoch by epoch bai, accoding o: hydoaic delay mapping funcion (iell [iell, 1996] mapping funcion i ued in GAPS). The paamee can be e a conan (e.g., ambiguiie and coodinae of aic poiioning), andom walk poce (e.g., neual amophee delay) o whie noie (e.g. eceive clock and coodinae in a kinemaic poiioning). The updae veco i compued uing lea quae echnique, accoding o: ( A PA + C ) A Pw =, (5) whee i he updae veco, A i he deign mai, P i he weigh mai, C i he paamee covaiance mai and w i he micloue veco. A evey epoch he paamee covaiance mai i updaed accoding o: ( A PA + C ( ) ) Cn C () = +, (6) whee C n i he poce noie mai, fo which he value vay depending on he ype of paamee, and () and (-1) ae epoch indicao of C. The micloue veco i compued in he ame way a in he igh hand ide of (3) and (4), wih he addiion of all neceay coecion: eah ide, anenna phae cene offe and vaiaion, aellie code biae (in cae C/A code i ued), phae-wind-up, elaiviic effec and agnac delay. A decipion of mo of hee coecion can be found in Kouba [23] and Téeaul e al. [25]. In Figue 1 i can be een a eie of even 24 hou oluion fo fome IGS aion UB1, uing GAPS in aic mode. The plo how he dfeence beween GAPS oluion and he efeence oluion, in hi cae, he IGS cumulaive oluion fo he ame week (conideed a ue hee). A P and + A y Y + A ρ + c d m T z Z + c dt + m =, (3) A + λ + A whee y = φ, Y + A z Z + c dt + m ρ + c d m T λ y, z, dt, and, (4) ae he compued updae fo eceive coodinae (X, Y and Z), eceive clock, neual amophee delay and ambiguiy paamee, epecively and m i he neual amophee non Figue 1. GAPS 24 hou oluion fo fome IGS aion UB1 (doy 91 o 97). A i can be een above, hoizonal coodinae have a diageemen of le han 2 cm, and heigh le han 5 cm.

3 The m value fo he hee componen ae 1.15 cm,.79 cm and 3.1 cm fo laiude, longiude and heigh, epecively. Figue 2 how an eample of coodinae convegence of a 24 hou oluion, in hi cae fo doy 91, aion UB1. A i can be een, hoizonal coodinae bee han 5 cm ae achieved afe aound 2 hou of obevaion in aic mode, and i ake a lile longe fo he heigh componen o achieve he ame eo level. I can be een ha afe 4 hou of obevaion hee i a vey mall impovemen in he hoizonal coodinae, while he heigh componen ake longe o fully convege. In he plo of Figue 2, he zeo value of he veical ae i he final value of each componen (no he IGS oluion, a in Figue 1). Laiude (m) Longiude (m) Heigh (m) Time (h) Figue 2. Coodinae convegence in aic mode (aion UB1, doy 91). A menioned befoe, GAPS ha alo he opion of poceing daa in kinemaic mode. In ode o acce i accuacy in kinemaic mode, daa colleced duing he Pince of Acadia pojec wa ued. In hi pojec a eceive placed on boad a boa avel beween he ciie of Sain John and Digby, hough he Bay of Fundy [Sano e al. 24]. Figue 4 how he ajecoy of he boa duing he day of analyi. In hi analyi he efeence oluion (conideed a ue ) i a mulibaeline baeline oluion povided by he ofwae Gafav veion 7.6 fom ovael. In hi cae, wo aic aion (in S. John and Digby) ae ued imulaneouly a efeence of he baeline, and moe weigh i given fo he neae aion. Figue 5 how he wo oluion (Gafav, in blue, and GAPS-PPP, in ed) fo laiude, longiude and heigh. Figue 4. Boa ajecoy in he Bay of Fundy. Figue 3 how he convegence of he neual amophee delay, a well a i andad deviaion. I can be noiced ha he neual amophee delay ake eveal minue o achieve i convegence AD (m) AD Sd. dev. (m) Time (h) Figue 3. eual amophee delay convegence wih GAPS. Figue 5. Gafav (blue) and GAPS-PPP (ed) oluion. Figue 6 how he dfeence beween he wo oluion fo laiude, longiude and heigh. The veical cale i he ame fo all hee componen (-3 m o 3 m). I can be noiced ha he heigh oluion i lighly noiie han he hoizonal componen. I can alo be noiced ha i ake aound one hou o achieve convegence.

4 φ = φ, (7) ( ) φ ( ) + λ whee φ i he meaued caie-phae fo eceive and aellie, φ ) i he eceive phae a ecepion ime, ( φ ( ) i he aellie phae a emiion ime and i an inege numbe of cycle. Howeve wha i in fac meaued a he eceive i he aellie phae a he ecepion ime, accoding o: Figue 6. Dfeence beween GAPS and Gafav oluion. Figue 7 how he ame eul a in 6, howeve dicading he wo fi hou and wih an enlaged veical cale (anging fom -.5 m o.5 m). The highe noie of he veical componen can be clealy een in hi figue. φ ( ) = φ ( ) φ ( ) + ρ, (8) + b b + c(dt d) + T I + λ whee eceive and aellie hadwae delay ( b and b ), clock eo, geomeic diance and amopheic efacion em have o be conideed. Equaion 8 i acually vey imila o (2), wih he incluion of phae, hadwae delay and ionopheic efacion em (Equaion 8 and fo each fequency, while 2 and fo ionopheic fee combinaion). Reaanging (8) imilaly o (2) lead o: φ ( ) = ρ + c(dt d) + T I + λ. (9) + ( φ ( ) + b ) ( φ ( ) + b ) Figue 7. Dfeence beween GAPS and Gafav oluion. The m value of he hee componen ae 6.9 cm, 5.5 cm and 13.9 cm fo laiude, longiude and heigh, epecively. A hown, GAPS povide poiioning oluion wih he epeced accuacy level fo a ae of a PPP package. Thi validaion i pimodial becaue GAPS i he ool ued fo he wide aea pecie poin poiioning model developmen, eplained in he ne ecion. Wide Aea baed Pecie Poin Poiioning A menioned ealie, he main goal of he wide aea PPP appoach i ecoveing inege ambiguiie paamee in PPP daa poceing. In ode o bee undeand wha i he elaion beween he inege ambiguiie and he PPP funcional model, we need o a wih he fundamenal caie-phae meauemen equaion: The above equaion can be conideed a he baic funcion model ued in PPP, wih he addiion of he aellie and eceive biae (including hadwae delay and phae). In fac we can conide one unique bia which include he wo menioned effec, ince hey can no be de-coelaed fom each ohe. Becaue of hi, fom now on we ae going o efe o hem a wo unique em, o be called eceive and aellie phae biae heeafe, a hown in (1): φ ( ) = ρ + c(dt d) + T I + λ. (1) + b b Becaue hee wo bia em ae no conideed in he baic PPP funcional model, when an ambiguiy paamee i eimaed, wha i being eimaed i in fac he ambiguiy plu he eceive and aellie biae. Theefoe, we ae uing PPP, we do no eimae ambiguiie, bu ambiguiy-like paamee. A i can be eaily noiced, equaion 1 can no be olved uing an iolaed eceive, becaue of he coelaion beween bia em and ambiguiie. Howeve he eceive bia can be handled wih an iolaed eceive, ince i i a common value fo all aellie. The eceive bia can be eihe eimaed a a paamee o eliminaed wih ingle dfeence beween aellie. Bu befoe ecoveing he

inege ambiguiy he aellie biae (dfeen fo each aellie) mu be known. The idea behind wide aea PPP i he deeminaion of aellie phae biae uing a wide aea newok of eceive.

5 inege ambiguiy he aellie biae (dfeen fo each aellie) mu be known. The idea behind wide aea PPP i he deeminaion of aellie phae biae uing a wide aea newok of eceive. Thee biae can hen be ued lae fo a eceive ouide he newok (a uly iolaed eceive) in ode o ecove he inege ambiguiy value. Figue 8 how an oveall flowcha of he wide aea PPP appoach. Figue 9. De-coelaion file (DCF) and PPP inide GAPS. Figue 8. Wide aea pecie poin poiioning flowcha. I i poible o ideny wo ak which ae no uual in em of PPP in he flowcha above. One of hem i he epaaion of a combined em, he dfeenial eceiveaellie bia (obained wih one unique eceive), ino wo em, fo aellie and eceive. Thi ak i no much dfeen fom wha i done when handling clock biae in a eceive newok, o handling newok dfeenial code biae in ode o eimae ionopheic delay. Theefoe hi i a ak fo which he oluion i known. The moe challenging ak in he flowcha above i he deeminaion of he dfeenial biae wih an iolaed eceive. Thi ak i ingulaly dficul becaue of eveal faco, including he fac ha he biae ae fequency dependen and hey ae coelaed wih ambiguiie and ionopheic efacion (ee fo eample equaion 9). In ode o ovecome hi dficuly a decoelaion file ha been being developed. The main ak of he de-coelaion file i o epaae he eceive and aellie biae fom ohe paamee, uch a ambiguiie and ionopheic efacion. Becaue he biae need o be lae ued wih caie-phae meauemen, ceain equiemen mu be aied o aue he compaibiliy beween he de-coelaion file and he obevable in which he biae deived fom ha will be applied, in em of qualiy. Thee equiemen ae (1) he ue of un-dfeenced caie-phae, wha will allow he ue of alo un-dfeenced caie a he iolaed eceive end; (2) he ue of un-combined caie-phae, which allow he ue of any combinaion a he poiioning ide, ince biae ae deemined fo each fequency epaaely; and (3) an eimaion independen of peudoange, o aue a low noie level and alo avoid peudoange biae. Figue 9 how he elaion beween he de-coelaion file (efeed o a DCF) and PPP inide GAPS. The file eceive infomaion fom PPP oluion, and povide he de-coelaed infomaion (ambiguiie plu biae and ionopheic advance). Wha i paed on fom he PPP o he file ae he adjued value of he eceive clock offe, neual amophee delay and coodinae. If hee em ae conideed a known in (1), he following equaion i obained: φ ) = λ ( I + + b b, (11) which i he funcional model of he de-coelaion file. The following ep ae he epaaion of he ionopheic delay (i can be called delay hee becaue i ha a negaive ign in equaion 11) fom he ohe em, and he lae epaaion of he inege ambiguiie fom he dfeenial eceive-aellie bia ( b b ). The epaaion beween eceive and aellie biae i done in a newok bai, a hown in Figue 8. The way he de-coelaion file wok will be eploed in deail in fuue publicaion, ince he main goal of hi pape i peening he oveall concep of he wide aea baed PPP appoach. Auming he ionopheic delay ae uccefully decoelaed fom he ohe em, one can ay ha he euling value i an un-biaed ionopheic delay. In ode o vey hi aemen, wo epeimen wee made. The fi epeimen i he daa poceing of wo aion (UB1 and UB3), which ae acually wo eceive haing he ame anenna hough a plie. The idea i ha he ionopheic delay ae uly bia-fee, he value compued fo boh aion hould be he ame. Figue 1 how he ionopheic delay obained fo he wo aion ove he day (doy 91).

6 newok eceive. Figue 12 how he eul of he facional dfeenial biae eimaion fo L1 fequency. Figue 1. Ionopheic delay fo aion UB1 (in blue) and UB3 (in ed). A i can be noiced, hee i a ceain ime needed fo he convegence achievemen, and afe ha he eimaed delay ae vey imila o each ohe. The econd epeimen make ue of wo IGS aion (CAGS and RC1) which ae appoimaely 2 km apa fom each ohe. Figue 11 how he ionopheic delay eul fo hee aion ove he day. Figue 12. Deeminaion of facional dfeenial biae fo aion UB1 and PR 2. In Figue 12 he uppe plo how he inege ambiguiy value, epeened by blue do. A i can be een, he ambiguiie aume dfeen value a each aellie paage, wih dfeence of eveal mee. The lowe plo how he facional dfeenial biae fo he ame day, whee i can be noiced ha he biae have a value flucuaing aound a mean value of.61 cycle, i.e., aound 3.9 cm a L1 fequency. The andad deviaion of he mean i.21 cycle. COCLUSIOS AD FUTURE WORK Figue 11. Ionopheic delay fo aion CAGS (in ed) and RC1 (in blue). Similaly o he fi epeimen, i can be noiced ha afe convegence he eul of he wo aion agee vey well wih each ohe. Thee eul how ha he ionopheic delay deived fom GAPS ae unbiaed, o in ohe wod, ha GAPS allow he deeminaion of caie-phae baed, un-biaed ionopheic delay. In ode o vey he facional biae obained fom he de-coelaion file ae meaningful, hey wee compued fo aion UB1 and PR 2, a evey aellie pa fom doy 91 o 97. The aumpion i ha he biae ae being coecly eimaed, hey hould be elaively able ove a few day. Thi aumpion i no eniely ue becaue pa of he biae ae hadwae dependen and hould have ome day o day vaiabiliy. Shae [1999] fo eample ha epoed a day-o day epeaabiliy of aound 3 cm o 9 cm fo he dfeenial code biae of he IGS In hi wok a new ofwae package fo GPS poiioning and daa analyi, called GAPS, wa inoduced. I wa hown ha GAPS povide poiioning eul a he epeced level fo a pecie poin poiioning ofwae, fo boh aic and kinemaic poiioning. Saic daa poceing (24 hou) howed m of aound 1 cm and 3 cm, fo hoizonal and heigh componen, epecively. Kinemaic poiioning unceainie ae aound 5 cm fo hoizonal componen and 15 cm fo heigh componen. I wa hown ha he ambiguiy paamee in PPP include aellie and eceive biae, which have o be adequaely epaaed in ode o obain inege ambiguiie, wha would allow ambiguiie fiing poce. In ode o do o, a new appoach wa inoduced, called hee wide aea pecie poin poiioning. The main idea of hi new appoach he deeminaion of aellie facional biae uing a newok of eceive. In ode o epaae facional biae fom ohe paamee uch a ionopheic delay and ambiguiie, a de-coelaion file wa ceaed. In epeimen caied ou involving neaby aion, and even aion haing he ame GPS anenna, he ionopheic delay deemined wih he de-coelaion file agee vey well wih each

7 ohe. Fom hee epeimen we can conclude ha GAPS i capable of eimaing caie-phae-baed, unbiaed ionopheic delay. Dfeenial eceive-aellie facional biae wee deemined fo fome IGS aion and PR 2 a L1 fequency. In hi epeimen 7 conecuive day of obevaion wee poceed. Ambiguiie and facional biae wee deemined fo each paage of he aellie. Alhough he ambiguiy value ae dfeen fo each paage, wih dfeence of eveal mee, he facional biae howed o be able wih a mean value of -.6 cycle, and andad deviaion of aound.2 cycle. Thi unceainy in meic uni fo L1 fequency i 3.9 cm, value which i in ageemen wih peviou wok in he lieaue epoing epeaabiliy of eceive dependen biae. The ne ep of he eeach i he efinemen of he decoelaion file, in ode o einfoce i cuen capabiliy of poviding eliable dfeenial facional biae and ionopheic delay, followed by an eenive daa poceing and eul analyi fo validaion pupoue. Once he compuaion of facional biae ae validaed, he newok adjumen will be pefomed in ode o epaae he aellie dependen biae, followed by hei applicaion in an iolaed eceive. Sano, M., D. Well, K. Cove, S. Binah (24). The Pince of Acadia GPS pojec: decipion and cienic challenge. Canadian Hydogaphic Confeence 24, May, Oawa. Shae, S. (1999). Mapping and Pedicing he Eah Ionophee Uing he Global Poiioning Syem. PhD hei, Univeiy of Ben, Ben, Swizeland, 228 pp. Téeaul, P., J. Kouba, P. Héou, and P. Legee (25). CSRS-PPP: An Inene Sevice fo GPS Ue Acce o he Canadian Spaial Refeence Fame. Geomaica, Vol. 59, o. 1, pp Zumbege, J.F., Heflin, M.B., Jeffeon, D.C., Wakin, M.M., and Webb, F.H. (1997). Pecie poin poiioning fo he efficien and obu analyi of GPS daa fom lage newok. Jounal of. Geophyical. Reeach, Vol. 12, o. B3, pp , AKOWLEDGEMETS We would like o acknowledge Piee Héou and Fançoi Lahaye, fo hei helpful dicuion. We alo would like o aknowledge he financial uppo fom CIDA (Canadian Inenaional Developmen Agency). Thi wok wa done unde GEOIDE pojec numbe 31 REFERECES Gao, Y. and Chen, K. (24). Pefomance Analyi of Pecie Poin Poiioning Uing Rea-Time Obi and Clock Poduc. Jounal of Global Poiioning Syem, Vol. 3 o. 1-2, pp. 95-1, 24. Kouba, J. (23). A Guide o uing Inenaional GPS Sevice (IGS) poduc. Publicaion of he IGS Cenal Bueau. Febuay 23. J. Kouba and P. Héou (21). Pecie poin poiioning uing IGS obi and clock poduc. GPS Soluion 5 2 (21), pp iell, A.E. (1996). Global Mapping Funcion fo he Amophee Delay a Radio Wavelengh. Jounal of Geophyical Reeach, Vol. 11, o. B2, pp

Relative Positioning Method of Using Single-frequency Model for Formation Flying Missions

Relative Positioning Method of Using Single-frequency Model for Formation Flying Missions Inenaional Induial Infomaic and Compue Engineeing Confeence (IIICEC 205) Relaive Poiioning Mehod of Uing Single-fequency Model fo Fomaion Flying Miion Hanyi Shi, Qizi Huangpeng2,a, Yuanyuan Qiao3,4, Yong